SCAN technology: Feature recognition in 3D-scanning.

A 3D-scanner measures distances from a plane or cylinder to points on 3D-objects. This gives a point cloud with up to several million points.
The problem is automatically to find features in such an image. Features could be objects like the centerline of ridges and valleys, and peaks and holes.

A more detailed description can be found as a postscript file

Danish Maritime Institute: Dynamic Positioning System.

The problem is how to most efficiently ensure that a ship, floating on the surface of the ocean, stays very nearly at rest with respect to the sea bed. One may employ thrusters, propellers and rudder action. More precisely, given external forces from wind, current and waves, and a specified position and motion envelope for the ship bulk, study the number, type, and placement of dynamic motion controls on the bulk with the goal of forming an optimal Dynamic Positioning System.

Danfoss: Scroll optimization.

Air-conditioning scroll compressors are manufactured by the million today and get greater and greater market shares from traditional (reciprocating) single piston compressors.

The scroll compressor consist of two plane spiral/helix running inside each other. Normally both scrolls are the same unrolling circle involute with constant wall thickness. The compression chambers are therefore thin, oblong, and bent. Often the one scroll is fixed and the other is orbiting.

The scroll compressor has its suction port at the periphery and discharge in the spiral centre. No suction valve is needed and a discharge valve is only present to decrease power consumption a little bit.

The scroll compressor has a rather constant speed of compression chamber decrease and thus a harmless almost constant torque loading of partly the electric motor and partly the housing (action and reaction).

Consequences of the scroll geometry are long gas leakage passages and high material temperatures in the scroll centre.

Different movements of scrolls are topics of today: Co-rotating and co-orbiting scrolls.

The task could be: Chose one scroll geometry and movements of both scrolls. Find the other scroll geometry (One scroll is envelope of the other). Scroll wall thickness could be a variable too. Make investigations and see how compressor performance/efficiency is influenced. Finally, find sensibilities and optimise design if possible.

LEGO: How to build with LEGO.

The idea for the project is simple - if any 3D body is given, how can it be built with LEGO bricks?

Unit-volume (the smallest possible volume) in the LEGO universe is a so-called "generic LEGO brick". It is a brick 8mm long and wide, and 3.2mm high, and has only one position ("stud") for connecting with other bricks. Although there are a lot of different LEGO bricks, in this project the use of "family" bricks only is allowed. "Family" LEGO bricks are paralelopiped-shape bricks that can be made of "generic" LEGO bricks, by putting several of them next to each other and/or above each other.
Allowed dimensions of "family" LEGO bricks are: (if the dimensions of the generic LEGO brick are set to 1,1,1)

length width height
1 1 1,3,15
2 1 1,3,6,15
3 1 1,3,15
4 1 1,3
8 1 1,3
10 1 1,3
12 1 3
16 1 3
2 2 1,3,9
3 2 1,3
4 2 1,3,9
6 2 1,3,9
8 2 1,3
10 2 1,3
12 2 1
16 2 1
4 4 1
6 4 1,3
8 4 1
10 4 1,3
12 4 1,3
6 6 1
8 6 1
10 6 1
12 6 1
14 6 1
16 6 1
8 8 3
16 8 3
24 12 3

Please note that some bricks appear in different heights. Length and width of bricks correspond to their number of studs (connection points) in the horizontal plane.

The usage of LEGO DUPLO bricks is allowed also. Dimensions of DUPLO bricks, in "generic brick" measure, are:

2 4 12
4 4 6,12
8 4 6,12
12 4 6
16 4 6
20 4 6

There is one important restriction here: Due to construction, DUPLO bricks can be connected only to family bricks with an even number of generic bricks in the length and width dimensions, and only with the bricks of height at least 3.

So the task is:

For a "legoized" 3D model (i.e. a 3D model that is represented as a set of 1x1x1 generic LEGO bricks put next to each other or above each other), find an algorithm to build the model of actual LEGO bricks from the previous tables, so that model should stand connected. We assume that a brick is connected to a model if at least two of its connection points are connected to a model. (If the brick has less than three connection points, then it is enough that only one of its connection points is connected to a model).

We do not want a model to be solid, meaning "full of bricks". Whenever it is possible to make an invisible hole inside a model, we would like it to be done - to spend less bricks in building. But all the bricks should be connected to the model as described earlier. A good "rule of thumb" should be that the width of the "wall" from outside to inside of the model is 4 connection points (it can be more or less in some places, the shape of the inside hole is not important).

We can assume nothing about the shape of a legoized object except that it is connected. It can have any number of holes into it (a cup with two handles, for example).

The preferred output of this project should be an algorithm for making a computer program for determining which brick should be put in which place. One of the problems we can see now is that there is not a unique solution - i.e. every model can be built using many different bricks. A criterion that "more solid" models are preferred can be used to set some cost-function. "More solid" models are models made with bigger bricks, and with bricks that have more connection points connected (and even these two criterions can be opposite!).

I have tried to explain here a problem as it appears in "real life". I hope this is enough for you to make an exact mathematical formulation of the problem (although I am aware that, as with all "real life" problems, some terms and requirements are not defined quite precisely - we require that the outside of the final model is exactly as in the legoized model, but we do not have such precise requests about the insides of the model, not even the precise thickness of the "wall" - but, these are facts of life!)

Grundfos: Mixing of clorine in swimmingpools.

Grundfos would like a model, describing the problem of mixing chemicals, being dosed into water systems, to be developed. The application of the model should be dedicated to dosing aqueous solution of chlorine into swimming pools.

The problem is imagined to contain two sub-models. The first model is concerned about dosing a strong aqueous solution of chlorine into a pipe system and the second about injection of purified and chlorinated water into the swimming pool.

The contamination of the water and the chemical process reducing the chlorine content in the swimming pool could be regarded as uniform and stationary and dependent of the number of bathers.

DANISCO: Temperature and moisture gradients in sugar silos

The distribution of heat and moisture in sugar stored in silos influence: The above, are important factors in sugar quality and production. In order to develop better silo operation strategies and silo designs, Danisco Sugar would like to develop a model that, with some accuracy, can predict the temperature and moisture gradients in bulk sugar.

The silos

Danisco Sugar utilises several types of silos for the storage of crystalline sugar. They differ in: The silos are filled during the beet-campaign (Sept.-Dec.), the sugar is withdrawn in a regular, but not constant, basis and the silos are emptied before next years campaign.

Temperature and moisture migration

Moisture gradients are created due to moisture migration in the bulk sugar by a variety of modes: Temperature gradients are induced by:

The models

The models should be able to predict temperature and moisture gradients in sugar silos by: The basic model could have the following features: A more advanced model could have the following additional features: A numerical model is sought that can be solved on a pentium PC if written in e.g. Turbo Pascal or Fortran. Models developed for corn silos can be used as an outset, e.g:

Tanaka H, Yoshida K (1984) "Heat and mass transfer mechanisms in a grain storage silo". Engineering Sciences in the food industry. Elsevier Applied Sience Publishers, Essex, England. pp 89-98

Khankari KK, Morey RV, Patankar SV (1994). "Mathematical model for moisture diffusion in stored grain due to temperature gradients". Transactions of the ASAE 37: 1591-1604)